Bison Maths Video on Mechanics

Introduction

• Second video in a series for A-Level Maths (Edexcel)
• Previous video on Pure Maths available on the channel
• Mechanics video focuses on simplifying topics into two main sections:
  • Kinematics: How things move
  • Forces: Includes connected particles, lifts, moments
• Upcoming video on Statistics
• Videos align with Pearson Edexcel textbooks
• Content also available for Further Maths

Mechanics Overview

• Simplifies mechanics into two major themes:
  1. Kinematics
  2. Forces

Kinematics

Key Concepts

• Constant Speed: Acceleration = 0
  • Distance = Speed × Time
  • Convert units between km/h and m/s
• Constant Acceleration: Use SUVAT equations
  • Know these equations by heart
  • Each equation is missing one of S, U, V, A, T
• Variable Acceleration:
  • Expressed in terms of t
  • Differentiate/Integrate to switch between displacement, velocity, and acceleration
  • Use unit conversion for memory aid

Graphs

• Speed-Time Graphs:
  • Area under the line = Distance
  • Acceleration = Gradient of the line

Vector Motion

• Use vector versions of SUVAT equations
• Resolve into horizontal and vertical components

Projectiles

• Combine no acceleration (horizontal motion) and constant acceleration (vertical motion)
• Use Pythagoras and inverse tangent for speed and direction

Forces

Modeling Assumptions

• Smooth Pulley: No friction, tension equal on both sides
• Light String: Tension is equal throughout
  • Inextensible String: Same acceleration for connected particles
• Particle: Ignore air resistance
• Rod: Rigid, no thickness

Equilibrium

• Words like static, at rest, constant speed imply balanced forces
  • Left=Right and Up=Down forces

Friction

• Opposes direction of motion
• Static: ≤ μR
• Dynamic: = μR

Connected Particles

• Resolve forces, apply F = MA
• Use vector addition for resultant force

Dynamics

• Use F = MA for resolving forces in direction of motion

Force Diagrams

• Show tension, thrust, and other forces on particles

Rigid Bodies

Uniform vs Non-Uniform

• Uniform: Weight acts at the center
• Non-Uniform: Weight does not act at the center

Tilting and Moments

• Moment = Force × Perpendicular Distance
• Conditions for equilibrium
  • Resolve forces horizontally, vertically
  • Take moments around a point

Conclusion

• Practice is crucial for mastering mechanics
• Video covers year one and year two content
• Encourages exploring additional resources on the channel